performance: A two-stage nonparametric approach

By M.T. Balaguer-Coll, D. Prior and E. Tortosa-Ausina

WORKING PAPER(2003/03)

ISSN 13 29 12 70ISBN 0 7334 2053 2

CENTRE FOR APPLIEDECONOMIC RESEARCH

On the determinants of local government performance: A two-stage

nonparametric approach∗

Maria Teresa Balaguer-Coll† Diego Prior‡ Emili Tortosa-Ausina†

May, 2003

Abstract

This article analyzes the efficiency of Valencian (Spain) local governments and their main explanatoryvariables. The analysis is performed in two stages. Firstly, efficiency is measured via (nonparametric) activityanalysis techniques. The measurement techniques also enable the sources of inefficiency to be identified, i.e.,whether inefficiencies are primarily overall cost, technical, or allocative. The second stage identifies somecritical determinants of efficiency, focusing both on political and fiscal policy variables. In contrast toprevious two-stage research studies, our approach performs the latter attempt via nonparametric smoothingtechniques, rather than econometric methods—such as OLS or Tobit related. Results show that inefficienciesare largely attributable to allocative factors, resulting in a notable gap between cost and technical efficiency.Inefficiencies are also larger for small municipalities. However they are not exclusively attributable to poormanagement, as second-stage analysis reveals both fiscal and policy variables, either within or outside localgovernments control, to be explicably related to municipalities’ performance.

Keywords: efficiency, kernel smoothing, local government, nonparametric regression

JEL Classification: D24, D60, H71, H72

Communications to: Emili Tortosa-Ausina, Departament d’Economia, Universitat Jaume I, Campus del RiuSec, 12071 Castello de la Plana, Spain. Tel.: +34 964728606, fax: +34 964728591, e-mail: tortosa@uji.es

∗We are grateful for the comments by George Battese, Tim Coelli, Kevin Fox, Quentin Grafton, Joseph Hirschberg and otherparticipants at the Economic Measurement Group Workshop ’02 held at the School of Economics, University of New South Wales,Sydney. Maria Teresa Balaguer-Coll and Diego Prior acknowledge the financial support of the Fundacio Caixa Castello (02I199.01/1)and the CICYT (SEC99-0771), respectively. Emili Tortosa-Ausina acknowledges the financial support of the Generalitat Valenciana(GV01-129) and the CICYT (SEC2002-03651).

†Universitat Jaume I.‡Universitat Autonoma de Barcelona.

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1. Introduction

All individuals, government, and firms have an interest, one way or another, in the achievement of efficiency and

productivity improvements in public sector activities. The study of public sector efficiency (or, perhaps more

appropriately, its inefficiency) is of paramount importance if we consider that bureaucrats may have an incentive

to waste resources, not to use inputs optimally and to produce too much, as claimed by Niskanen (1975) or

Breton and Wintrobe (1975), amongst others. This ability shown by bureaucrats in pursuing objectives that

are not in the interest of the citizen-voters may not be unlimited (Grosskopf and Hayes, 1993). For these and

related, reasons, many research studies have analyzed different aspects of efficiency and productivity in various

public sector areas as important as health, education, taxation or, in the case we are dealing with, different

government departments such as municipalities.1 In many cases these attempts have been pursued using frontier

techniques, both parametric and nonparametric.

Previous literature on the efficiency and productivity of municipalities all over the world consists of research

studies which vary widely in many aspects, ranging from their aims to their conclusions. This literature is not

abundant, although some relevant contributions have lately been published. Studies which are closer to both our

attempts and techniques are, amongst others, De Borger and Kerstens (1996), De Borger et al. (1994), Hayes

and Chang (1990), Deller (1992), Deller and Rudnicki (1992) or, more recently, Worthington and Dollery (2002).

For an excellent survey of frontier efficiency measurement techniques in local government see Worthington and

Dollery (2000). Other related studies are those by Davis and Hayes (1993) or Grosskopf and Hayes (1993) and,

in general, the literature on local government efficiency and property values. We should also note that some

studies focus on the efficiency of a single service rendered by local authorities, although this depends critically

on the services and competencies of local authorities, which differ widely from country to country.

The translation of the production process at municipal level in terms of the standard notion of transforming

inputs into outputs very often presents a huge problem. In the case of municipalities it is quite common to

distinguish three stages in this production process (Bradford et al., 1969). First, there is the transformation

of primary inputs (labour, equipment and external services) into intermediate outputs (e.g., hours of traffic

control or the extension of police services). Second, these intermediate outputs are transformed into direct

outputs (D-outputs as termed by Bradford et al., 1969) ready for “consumption” (e.g., the number of urban

streets controlled or the number of cases treated). Third, these direct outputs ultimately have welfare effects

on consumers (e.g., increasing perceptions and feelings of safety and welfare). This final process is captured

by outcome indicators (labelled C-outputs by Bradford et al., 1969) that reflect the degree to which the direct

outputs of municipal activities translate into welfare improvements as perceived by consumers. Theoretically,

efficiency can be measured at each stage of this production process. Yet in practice, data availability problems

typically do not allow us to distinguish between primary inputs, intermediate outputs, direct outputs, and final

welfare effects. For this reason the analysis is very often limited to the study of the first and second phases of

this process: relations between primary inputs or activities and direct outputs.

In this article we focus on the efficiency of Valencian (Spain) local governments. In this case the literature is

1An excellent introduction to these topics is provided by Fox (2001).

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much scarcer. However, the study of Spanish local government efficiency is relevant for several reasons. Amongst

them, we find that the decentralisation of public responsibilities to lower levels of government has been growing

at a fast rate in Spain over the last few years,2 fuelling the debate on operational efficiency in local governments.

During the last twenty-five years, both regional and local administrations in Spain have gained competencies

at the expense of central administration, especially since the late seventies, following the establishment of

democracy. Specifically, the Spanish Constitution granted higher independence to state and local governments,

Comunidades Autonomas—states or regions, NUTS2 in European terminology—, Provincias—provinces, or

NUTS3—, and Municipios—municipalities, or NUTS5 (Prieto and Zofıo, 2001). Proponents of decentralization

of public functions to lower levels of government may argue that local responsibility contributes not only to a

better match between public services and the needs or preferences of a diverse citizenry, but also as an effective

way to control the overall growth of government (Deller, 1992; Marlow, 1988). Indeed, if effective policy is to be

formulated, it becomes necessary to improve our understanding of managerial capacity in local governments, due

to the increase in functions deriving from decentralization. However, the literature on the relative superiority

of a city manager form of government is inconclusive (Hayes and Chang, 1990) as, on the other hand, some

authors argue that the small size of operation for many local governments in inherently inefficient in economic

terms, and hence costly.

Other papers dealing with the analysis of efficiency in Spanish municipalities are those by Prieto and Zofıo

(2001) and Gimenez and Prior (2001), and differ from ours in several aspects, including the regions studied.

Our study focuses on the Valencian region,3 whereas theirs considered Castilla-Leon and Catalonia, respectively.

Unfortunately, the type of information provided for Spanish municipalities is often different for each region, and

very difficult to homogenize, which confines us to the analysis of a single region. There are other works that

evaluate Spanish local services, but all of them concentrate on the evaluation of specific services: garbage

collection, urban public transport, water supply, local police, fire service, etc. An alternative perspective is

presented here, with a focus on the evaluation of local organizations as a whole, such as decision-making units

that organize the production process of multiple services (although in some cases only through finance and

control but not management). There is, therefore, a risk of classifying a council as inefficient in spite of the

fact that some of its services may be well managed. This gives rise to the typical discussion on whether the

evaluation should concentrate on basic production plants (understanding “efficiency” as it is applied to fields

such as engineering) or, on the contrary, whether it is reasonable to analyze the efficiency of more complex

organizations that share common strategic objectives. As mentioned above, this study has opted to carry out

a global analysis, relating research to that of Vanden Eeckaut et al. (1993) and De Borger and Kerstens (1996)

although with significant and specific methodological contributions.

This decision has both positive and negative aspects. On the positive side it should be stressed that each

council receives a global efficiency score representing the weighted average efficiency of the different services

provided. Furthermore, although it may appear paradoxical, by opting for the evaluation of more disaggregated

2Similarly to what occurred in the U.S., where one of the legacies of the Reagan Administrations was the decentralisation ofpublic functions to lower levels of government.

3Located along the Spanish east coast, with a very dynamic economy. In terms of other Western European countries, it has apopulation roughly comparable to that of Ireland or Norway, and it accounts for approximately 10% of total population in Spain.

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decision-making units, the analysis of the results obtained could be extremely controversial. For instance, if the

information required is not directly available, the application of ungranted cost-accounting imputation criteria is

needed to estimate the inputs consumed. This fact is especially important in the sector analyzed, given that, to

date, the spillover of cost-accounting practices in Spanish municipalities is very limited. The negative aspect of

the decision lies in the selection of representative variables for the output, as our choice must be representative

of the global level of services. This fact hinders further diagnosis of precisely those services which require better

management. To summarize, the analysis of specific services provides an acceptable evaluation of production,

although all the factors that are actually consumed cannot be analyzed. The choice of the alternative option,

however, presents weaknesses on the production side, although the determination of the inputs is more exact.

We focus not only on efficiency but, more importantly, on its determinants. In this case, as suggested by

De Borger et al. (1994), we find that many studies dealing with estimating inefficiencies in the public sector

“simply do not attempt to explain the estimated inefficiencies in a systematic way”. In other words, it may also

be of interest to determine whether some factors, either discretionary or beyond the control of local managers,

may affect the performance of municipalities. This is the spirit of the so-called two-stage, or two-step analyses.

On this point, previous literature has focused less thoroughly on the determinants of inefficiency. However,

our study differs substantially from previous contributions4 in the techniques we employ. Those considered

to measure efficiency are fairly standard. Specifically, we use the nonparametric DEA (Data Envelopment

Analysis) technique, which is quite often employed in public sector studies. However, we also use a set of

nonparametric techniques to analyze the determinants of efficiency, based on previous work by Deaton (1989),

DiNardo et al. (1996), or Marron and Schmitz (1992), amongst others, in contrast to the more common set of

parametric techniques—such as OLS, or Tobit censored regression model—used in the two-stage analyses. These

techniques focus on graphical aspects of efficiency results, which provide a great deal of meaningful information,

and which may be particularly relevant in our setting, given the peculiar distributions of DEA efficiency scores,

which are bounded at unity.

The study is organized as follows. After this introductory section, section 2 introduces the model for

measuring efficiency. Section 3 presents the data, inputs and outputs definition, and results. Section 4 sets out

both the different explanatory variables for efficiency and the techniques to be employed in the second-stage

analysis, together with some results. Finally, section 5 outlines the most relevant conclusions.

2. Overall cost, technical, and allocative inefficiencies

In principle, measurement of efficiency notions is easy if reliable data are available on both quantities and prices

of all inputs and outputs. When some necessary information is unavailable, then we are restricted in the type

of efficiency that can be measured. For instance, technical efficiency solely requires data on inputs and outputs,

while allocative efficiency requires additional information on input prices. If data on costs are available, but

data on prices and physical units are not, cost efficiency can be evaluated, but its decomposition into allocative

and technical dimensions cannot. However, if we assume that all Decision Making Units (DMUs) face the same

4Such as, for instance, the application of De Borger and Kerstens (1996) for Belgian municipalities.

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input prices, this decomposition can take place. Consequently, the type of information available determines the

flexibility of performance measurement.

To introduce some notations, let us assume that for S observations there are J inputs producing I outputs.

Hence, each s observation uses an input vector xs = (xs1, . . . , x

sj , . . . , x

sJ ) ∈ R

J+ to produce an output vector

ys = (ys1, . . . , y

si , . . . , y

sI) ∈ R

I+. Production technology is defined by the set of feasible input and output vectors:

F = {(x,y)|x can produce y}. (1)

It is also useful to consider the output and input sets associated with this technology. For a given input

vector xs, the output set denotes all output vectors (y) that can be produced from the given input vector xs:

P (xs) = {y|(xs,y) ∈ F}. (2)

Also, for a given output vector ys, the input set denotes all input vectors x capable of producing the output

vector:

L(ys) = {x|(x,ys) ∈ F}. (3)

The next theoretical building block is the cost efficiency measurement. Treating outputs ys as given, we can

compute for each observation s the minimum expenditure (psx) to produce observed output vector (ys):

TC∗(ys,ps) = min{psx|x ∈ L(ys)}. (4)

According to Fare et al. (1995), the minimal cost may be calculated as the solution to the linear programming

problem:

TC∗(ys,ps) = min psx

s.t. x − λN ≥ 0,

−ys + λM ≥ 0,−→1 λ = 1,

(5)

where N is a matrix containing the observed S input vectors, M is a matrix containing the observed S output

vectors and λ is the activity vector denoting the intensity levels at which the S observations are conducted.5

As previously mentioned, when information on input prices and input quantities is not available, all units are

assumed to face the same input prices, and we operate with input costs variables.

With TC∗(ys,ps), the overall cost efficiency measure OEs can easily be defined as the ratio of minimum

cost (psx) to observed cost (psxs), i.e., OEs = psx/psxs. Computing the individual cost efficiency scores

requires program (5) to be solved for each s observation, or DMU, in the sample. The value of OEs is smaller

than unity for inefficient observations, and equals unity for efficient observations.

5The constraint−→1 λ = 1 accounts for the assumption of variable returns to scale (VRS). By removing such a constraint we

would assume constant returns to scale (CRS) technology. The CRS technological assumption is only appropriate when all firmsare operating at an optimal scale. Such an assumption does not hold for Spanish municipalities, as shown by Balaguer-Coll et al.(2002).

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Overall cost efficiency is the multiplicative result of technical efficiency (TE) and allocative efficiency (AE):

OEs = TEs · AEs (6)

Allocative efficiency requires there to be no divergence between observed and optimal input mix. A municipa-

lity is allocatively inefficient otherwise. Overall and allocative efficiency imply price-dependent characterizations

of efficiency, while technical efficiency is an entirely price-independent notion.

A more informal definition of the decomposition first requires the specification of the nonparametric tech-

nology with variable returns to scale technological assumption:

F = {(x,y)|x can produce y} = {(x,y)|λN = x ≤ xs, λM = y ≥ ys,−→1 λ = 1}. (7)

Using this technology, the decomposition is implemented as follows. Technical efficiency is evaluated relative

to this technology and allocative efficiency is derived from dividing overall efficiency by technical efficiency. In

order to quantify this decomposition we must solve a new linear program that quantifies the technical inefficiency

coefficient:TEs(ys,xs) = min ρs

s.t. ρsxs − λN ≥ 0,

−ys + λM ≥ 0,−→1 λ = 1.

(8)

Like the OEs coefficient, the value of TEs is smaller than unity for technically inefficient observations, and

equals unity for technically efficient DMUs. Finally, the allocative inefficiency, due to problems with the observed

input mix, is calculated residually from overall cost and technical efficiency coefficients, i.e., AEs = OEs/TEs.

So far we have introduced the so-called Farrell-Debreu’s idea of efficiency (Farrell, 1957). Yet there exists

a more urgent concept based upon the Pareto-Koopmans’ idea,6 which makes allowances for the possible input

excesses, or output shortfalls, represented by s− ∈ RJ and s+ ∈ R

I , respectively. If these components are to be

computed, program (5) becomes:

TC∗(ys,ps) = min psx − ε−→1 s+

s.t. x − λN = 0,

−ys + λM − s+ = 0,−→1 λ = 1,

(9)

whereas program (8) becomes:

TEs(ys, xs) = min ρs − ε−→1 s+ − ε

−→1 s−

s.t. ρsxs − λN − s− = 0,

−ys + λM − s+ = 0,−→1 λ = 1.

(10)

6“Pareto-Koopmans efficiency” is the production economics analogous to the more widely known concept of “welfare efficiency”used in economics.

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where ε is an infinitesimal constant introduced so as to provoke a second stage movement via the slack variables,

s+ and s− (see Cooper et al., 1999).

3. Computing efficiency measures for Spanish municipalities

3.1. Data, inputs, and outputs

The different types of data we will deal with throughout the paper were provided by different institutions.

Inputs came from the budget data of local authorities in the Valencian region, which presented information to

the Valencian Audit Institution in the year of study (1995). On the other hand, the outputs were obtained

from information gathered in a survey of local infrastructure and equipment devised by the Spanish Ministry

for Public Administration. Due to data unavailability, our focus is entirely confined to the year 1995, since

output values are only available for that year.

As stated by Fox (2001), it is difficult to measure the inputs and, more especially, the outputs of a hospital,

a police force, or a government department. This was also reflected long ago in, for instance, the studies by

Bradford et al. (1969), or Levitt and Joyce (1987). It also often constitutes a serious source of controversy.

Fletcher and Snee (1985) have ranked what hinders output measurement in the public sector, by considering

firstly problems in setting the objectives, and secondly problems in measuring the outputs themselves. Given

our aims, and considering we are dealing with municipalities, we are not free from criticism. However, in many

cases this criticism is leveled as a result of limitations in the database, or simply because of variables which

can hardly be justifiable as outputs. On this point, we must acknowledge the virtues of our database, which

provides not only quantities for each output but also includes an indicator of quality (good, average, or bad),

which turns out to be crucial for assessing local government performance.

Our selection of inputs is based on budgetary variables that reflect municipalities’ costs. These are imple-

mented rather than forecasted expenditures, given the usual discrepancies amongst these figures. It is often the

case that forecasts underestimate expenditure and overestimate revenues. In contrast to many other studies, we

included capital measures—capital expenditures and capital transfers. Descriptive statistics for the year 1995

are provided in Table 1. This choice implies certain problems, as in many instances costs are shared by several

government departments.

The selection of outputs is based on the minimum services provided by each municipality. Specifically, all

local authorities must provide public street lighting, cemeteries, waste collection and street cleaning services,

drinking water to households, access to population centers, surfacing of public roads, and regulation of food

and drink. In some cases we have to select proxies for these services. For instance, as pointed out by De

Borger and Kerstens (1996), population is assumed to proxy for the various administrative tasks undertaken

by municipalities, but it is clearly not a direct output of local production. Other important outputs, such as

provision of primary and secondary education, do not come within the responsibilities of municipalities. The

list of outputs for 1995, along with summary statistics, is displayed in Table 1. Table 2 also enumerates what

service attempts to measure, or to proxy, each output indicator.

We also include an interesting variable aimed at measuring not only the quantity but also the quality of the

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services provided. This unusual type of data turns out to be very informative for municipality output. It is often

the case that each local government cannot directly affect, at least in the short-run, the quantity of outputs

such as street infrastructure surface area or the registered surface area of public parks. However, it may have

a decisive impact on their quality. The information available on this variable is of a categorical nature—the

quality of the services offered is arranged in three classifications: good, average or bad. It is quantified using

the proposal set out by Banker and Morey (1986b), which involves breaking down the quality variable into two

categorical variables, d1 and d2. Thus, for unit s, the values taken by d1 and d2 are ds1 = ds2 = 0, if the quality

is bad, ds1 = 1 and ds2 = 0, if the quality is average, and ds1 = ds2 = 1, if the quality is good, weighting for each

output’s share. Hence, our model includes both production and quality variables, enabling a joint assessment

of both efficiency and quality to be made.

3.2. Results

We estimate a common frontier for the year 1995. Results are presented in Table 3. It shows not only simple

summary statistics such as mean and standard deviation but also additional statistics which provide further

insights into the distribution of efficiency scores. Since the distribution of efficiency measures is skewed, it is of

interest using other statistics, such as the median, for a better understanding of what efficiency indices reveal.

We also considered that providing results for the different size classes was of interest.

Out of 414 observations, only 32 (7.73%) were found to be cost efficient—i.e., had an efficiency score of 1.

Efficiency is enhanced when costs are handled separately and, consequently, technical efficiency is evaluated, for

which we find 144 efficient municipalities (34.78%). There are exactly the same number of allocative inefficient

units, since allocative inefficiency is computed residually. Therefore, there is a notable gap between overall cost

and technical inefficiency attributable to allocative reasons. Specifically, average cost efficiency is 53.1%, whilst

average technical inefficiency is 80.1%. Hence, each municipality’s specific input mix has quite an effect on its

level of cost inefficiency. A sound reallocation of resources would probably lead to a substantial increase in the

cost efficiency of many municipalities.

Table 3 also shows that the highest levels of efficiency are found amongst the most highly populated muni-

cipalities. Of special note is the technical efficiency for cities with more than 20,000 inhabitants, whose average

efficiency is 96.8%. On the other hand, overall cost efficiency is quite low for the smallest group of municipalities

(on average, 42.8%). This is also the group of municipalities that shows the greatest disparities amongst DMUs

in the group. In addition, small municipalities are those with higher allocative inefficiency, probably stemming

from the fact that this is the group of municipalities facing greater difficulties in reallocating inputs in order to

achieve cost reductions, given their lower negotiation power. In fact, differences between the most populated and

the least populated municipalities are much higher for allocative efficiency (0.887 vs. 0.554), than for technical

efficiency (0.968 vs. 0.792, respectively). Furthermore, we should also bear in mind that municipalities with

populations of under 5,000 do not have to disclose as much accounting information as those over 5,000, which

could lead to less effort being made to monitor expenditures.

We also provide Tukey’s box plots to attain a more in-depth interpretation of results. They are particularly

informative in the case of efficiency scores obtained via linear programming techniques, which are bounded

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by zero and unity, and for which a mass of observations achieves the upper bound, typically yielding skewed

distributions. Yet as suggested by Lovell et al. (1994), skewness of DEA scores is rarely reported, “and even

more rarely put to any good use”. We report box plots since they disclose a more scrupulous illustration of

the distributions, consequently encoding further information on the features possibly hidden by data, such as

multi-modality or the existence of outliers, which may have quite an impact on mean efficiency—along with the

aforementioned mass of scores at unity.

Box plots are shown in Figure 1 for each size class and the interpretation is straightforward. For each size

class, the box represents the 50% mid-range values of the efficiency scores. The length of each box represents

the interquartile range (IQR). The line breaking down each box represents the median. The whiskers define the

natural bounds of the distributions, i.e., the mean±IQR, while the short lines represent outliers lying outside

the natural bounds.

It can be observed from the IQRs that the distribution of efficiency scores steadily shrinks with size. The

most inefficient observations are found amongst the smallest size classes, especially amongst those municipalities

with fewer than 1,000 inhabitants. On the other hand, most of the largest municipalities are efficient. Indeed,

all inefficient municipalities in this size class are classified as outliers. However, given our variable returns to

scale assumption, this inefficiency does not take problems of scale into account, and only compares entities with

those of similar sizes. Therefore, although it seems that larger municipalities are closer to the frontier due to

their greater resources (qualified staff, better information technology resources, etc.), we must bear in mind the

scale effect, i.e., we are comparing equals.

Technical inefficiency is generated due to a failure in the use of the different inputs required in the production

process. Yet the efficiency measures we have computed so far do not inform on what the greatest sources of

input waste are. We already know there is a notable disparity between cost and technical inefficiencies due

to allocative reasons, but nothing is known about exactly which inputs are those inputs whose use might be

optimized to a greatest extent. This type of information is summarized by the input and output specific

inefficiencies, representing input excesses and output shortfalls, respectively. Indeed, some authors argue that

any non-zero input or output specific inefficiencies should be reported so as to provide an accurate indication

of a municipality’s technical efficiency.

Table 4 reports summary statistics for input specific inefficiencies, or input excess, indicating whether ex-

cessive use of specific resources exists. Figures closer to zero indicate optimal behavior (no waste of inputs),

whereas figures closer to one indicate greater input waste. For all input variables, we find similar average values,

ranging from 21.2% to 24.7%—except for capital transfers (X4), whose average input excess is only 11.7%. A

meticulous scrutiny of each figure displayed in Table 4 reveals that, once more, large cities (in terms of popu-

lation) show the leading performance. Yet we can also observe that the two least populated categories show a

similar behavior.

The lower value of X4 with respect to X5 could give a misleading impression, given that both variables are

related to capital expenditures. A deeper scrutiny of both variables suggests X4 refers to external transfers (to

firms, etc.), whereas X5 is related to direct transfers to the council. The emerging picture seems to suggest that

the expenditures which are not to be invested in the municipality itself are managed more diligently, so as to

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minimize this type of expenditures.

Of special note is also the high value found for X3, encoding current transfers, which could stem from the

tendency of some municipalities to confer public services to other firms and organizations, either public or

private. An input excess could therefore imply that some public contracts are awarded inefficiently. Yet for

large municipalities X3 holds the lowest value, suggesting either that external firms are not contracted, or that

these firms and/or organizations perform their tasks much more efficiently, given the tough competition they

face from other possible firms being contracted.

Table 5 discloses results for output shortfalls, or underprovision of outputs. Optimal behavior must be

interpreted the other way round, as figures closer to zero indicate stronger underprovision of outputs. In

some cases, the interpretation of certain results is slightly critical. For instance, a DMU for which variable Y1

shows an indicator below unity would indicate that this municipality is “underproviding” population. In the

case of Y3, the output not provided in sufficient amount is “tones of waste”. Yet both Y1 and Y3 show the

lowest shortfalls—the indicator is close to unity. This would imply that for the amount of services provided,

population could be higher. On the other hand, both Y2 and Y4 exhibit the highest shortfalls—as shown by

lower indicators, i.e., closer to zero. This means that the most underprovided outputs are the number of lighting

points and street infrastructure surface area, respectively, which particularly holds for small municipalities.

This explanation coincides with that for input excesses, as small municipalities do not manage variable X5, i.e.,

capital expenditure as efficiently. However, this also occurs because small municipalities require higher capital

expenditures per capita.

4. Efficiency explanatory variables

DEA computations yield only a first-stage, first-order, or first-step measure of relative efficiency. What is not

known is the reason for variations in such efficiency patterns, and it is clear that computing individual efficiency

scores may not be enough for either consulting purposes or for policy analysis. Accordingly, a second-stage

analysis is called for, as efficiency may be affected not only by inadequate management but also by exogenous

factors beyond the control of each local government. As Lovell et al. (1994) pointed out, such ideas had been

already considered by Lewin and Minton (1986) in their research agenda, calling for studies aimed at illustrating

the “feasibility of using DEA (perhaps in combination with other analytical methods) as a mathematic for

relating effectiveness outcomes to features of organization design”.

In our search for explanatory variables we considered the information provided by the Valencian Audit

Institution on different financial and budgetary, fiscal policy, variables, such as tax revenue, grants, or financial

liabilities. We also considered a political variable which is the percentage of votes of the governing party from

the total votes in each municipality. This is a group of factors over which a local government may exert certain

managerial control. However, others may be thought of as nondiscretionary, or exogenous.7 The expected

7However, the term nondiscretionary is usually employed only when referring to inputs used in the production process. Speci-fically, nondiscretionary inputs are those beyond the control of a DMU’s management. For example, Banker and Morey (1986a)illustrate the impact of exogenously determined inputs that are not controllable in an analysis of a network of fast food restaurants,where four out of six inputs were not controllable by each unit’s management: age of store, advertising level, urban/rural location,and drive-in capability.

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impact of each factor on the efficiency scores is commented on below.

Of the fiscal policy variables the first one to be considered is tax revenue per capita (TAXES). We may

hypothesize a negative impact on efficiency, as it seems reasonable that a local government that is highly

capable of generating revenues would be less motivated to manage them efficiently. This idea also comes from

the property rights and principal-agent literature, which outlines several reasons why politicians and public

managers may lack proper incentives to effectively audit and control expenditures (De Borger and Kerstens,

1996). On the other hand, high taxes may increase voters’ awareness of control of public expenditure (Davis

and Hayes, 1993). Yet such an awareness might, instead, worsen efficiency, and the situation could occur that

bureaucrats had a preference for more visible inputs rather than those which are less tangible, since they are

easier to justify in the appropriation process (Lindsay, 1976). For instance, police cars may be more visible

than training.

The second fiscal policy variable to be considered is transfers, or grants, divided by population (GRANTS),

representing transfers received from higher layers of government, which depend on variables such as number

of inhabitants, number of schools, etc. More than 70% of these grants are unconditional grants for current

spending. They also account for nearly 40% of total non-financial revenues of Spanish municipalities. Following

Silkman and Young (1982), this variable may be regarded as having a negative association with efficiency, as

the cost of inefficient behavior is increasingly shared by a broader constituency.

Thirdly, self-generated revenues (divided by population) (SELFG), which include not only general taxes

but also other revenues such as those from taxes on personal wealth or fortune and local government property

transfers, which share the common feature of being self-generated by each municipality. Therefore, this variable

partially overlaps with TAXES, and the likely impact is expected to be similar, although in this case the

intensity of monitoring by the citizens’ effect (Davis and Hayes, 1993) is partially lessened.

Local governments with lower fiscal revenue capacity will probably be impelled to follow alternative paths

to raise revenues, such as issuing securities or making loans. To proxy for these effects, we include the variable

SECLOAN , which measures income generated by issuing debt and making loans, divided by population. Its

impact on efficiency is not a priori obvious. We may hypothesize that the municipalities that issue bonds and

securities are those unable to raise revenues via taxes. In such a case, the taxpayers’ incentives to effectively

control expenditures may be low and, consequently, we might expect a negative relationship with efficiency. On

the other hand, this variable is assumed to be inversely related to TAXES and SELFG, as the municipalities

with higher levels of issued securities are possibly those unable to generate revenues in more traditional ways—

i.e., taxes. In such a case, the impact over efficiency would be positive.

Another variable to be included is total expenses divided by total revenues (DEFICIT ), which proxies the

idea of deficit—although defined in a different way—and is expected to be negatively associated with efficiency.

As deficit increases, we may face a higher social awareness to encourage its reduction; in such a case, local

governments may adopt strategies to enhance efficiency. Municipalities carry on activities within the framework

of a financial contingency which requires a balance between their receipts and their expenditures, the rupture

of which can put them in a situation of financial vulnerability. This may be due to inefficient management,

or simply to structural insufficiency of resources. Thus, one may hypothesise an inverse relationship between

11

efficiency and financial vulnerability. If we define financial vulnerability as the inability of a municipality to

face its present and future financial commitments as they fall due, we may consider deficit a good proxy for it.

Apart from these fiscal policy variables, we have included a political variable representing the relative

importance of votes held by the governing party divided by population (V OTES). If the governing party has

an absolute majority, other parties or coalitions will possibly face greater difficulties in effectively controlling

expenditures. Efficiency might not be the criterion used when awarding contracts for public works or building

permission, hiring new workers, or setting local managers wages, with the possible result that court orders

are the only way to control this expenditure. In such a case the expected association between V OTES and

efficiency would be negative. However, one might alternatively hypothesize a positive association since city

managers would have an incentive to lower costs and increase efficiency in order to ensure their job security.8

4.1. Kernel contributions: nonparametric kernel regression and bivariate density functions

As shown in section 3 in the Tukey’s box plots, it may easily be inferred that the distributions of efficiency scores

differ substantially from the symmetric Gaussian bell-shape distribution. In such a case, it may be potentially

erroneous to consider OLS, given the assumptions inherent in this technique. Accordingly, previous research

studies performing this type of two-stage analysis consider alternative estimation techniques, such as the Tobit

censored regression model so as to accommodate the efficiency scores at unity. Unfortunately, this alternative

method may have further disadvantages as to the (likely) correlation between the efficiency scores and the

explanatory variables (see De Borger and Kerstens, 1996). Some other authors (see Charnes et al., 1988) have

addressed the violation of normality assumption by employing the L1-metric regression. Alternatively, Lovell

et al. (1994) construct modified DEA efficiency scores (MDEA efficiency scores) which are only bounded by

zero, following Andersen and Petersen (1993), whereas Ray (1991) considers a variant of corrected least squares

in the second stage.

Furthermore, the efficiency scores generated by DEA, in the same manner as other nonparametric techniques

for efficiency measurement, are clearly dependent on each other in the statistical sense. The calculation of each

DEA efficiency score for one municipality involves all the other municipalities in the observation set. This

circumstance indicates that the potential regression analysis results, as one of its basic model assumptions is

not met. Whether we consider OLS or Tobit models, in both cases disturbances are assumed to be i.i.d drawings

from a normal distribution. Since the distributions of both the dependent variable and the disturbances are

the same (only their means are different), we are assuming that the efficiency scores are independent, which

is not true. In addition, as outlined by De Borger et al. (1994), it is well-known that the Tobit estimates are

sensitive to any violation in the underlying assumptions. These ideas have been forcefully made by Harker and

Xue (1999), who suggest a bootstrap methodology so as to address the problem.9

These somewhat troublesome issues have led us to consider an alternative set of techniques for disentangling

the variables representing the factors likely to impact on efficiency performance of local governments. Specifica-

8Obviously, the most desirable variable would be a dichotomous variable, taking values one or zero depending on whether anabsolute majority governs the council. Unfortunately, that type of information is unavailable to date.

9The fragility of regression estimates has been reported not only in the efficiency literature but also, for instance, in Leamer andLeonard (1983).

12

lly, we consider both nonparametric regression and nonparametric density estimation, which are less powerful

in terms of prediction yet extremely informative for explanatory purposes. They are particularly useful in the

case of local government studies where the number of observations is usually large. They build on previous

work from authors such as, for instance, Deaton (1989), DiNardo et al. (1996) or Marron and Schmitz (1992).

Their main advantage is their nonparametric nature, conferring them an ability to provide easily comprehended

graphical descriptions of the data that are directly informative about the problem in hand. In addition, this

methodology is relatively robust to outlying observations.

4.1.1. Nonparametric kernel regression

In econometrics, the assumption of statistical adequacy or correct specification has been a constant concern for

some time now. This concern is present in our setting, for the reasons set out above. In fact, as Haavelmo

(1944) asks, “what is the use of testing, say, the significance of regression coefficients when maybe the whole

assumption of the linear regression equation is wrong?” (Haavelmo, 1944, p. 66). The peculiar structure of our

data, made explicit in Figure 1, puts forward the employment of nonparametric techniques, which allow us not

only to relax the assumptions of the underlying model, but also help in corroborating the goodness (or lack) of

fit of parametric specifications.

The basic purpose of a regression analysis is to study how a variable Y , in our case efficiency estimates,

responds to changes in another variable X. So as to prevent convoluting notation, these two variables will be

labeled EFF and z, respectively, where EFF may refer to either overall cost, technical, or allocative efficiency.

If we have data on these variables, then smoothing of a data set {(Zs, EFFs)}Ss=1 involves the approximation

of the mean response curve m in the regression relationship:

EFFs = m(zs) + εs, s = 1, . . . , S. (11)

where εs represents the error term. The less we know about the nature of m, the more desirable a nonparametric

estimation approach is. These methods impose a minimum of structure on the regression function. Therefore,

the main advantage of this technique is that the data are allowed to choose the shape of the function, and there

is nothing that forces the points to lie along a straight line, or along a low-order polynomial (Deaton, 1989).

Nonparametric methods are also known as smoothing methods, i.e., methods aimed at sanding away the rough

edges from a set of data or, in other words, to remove data variability that has no assignable cause and to

thereby make systematic features of the data more apparent (Hart, 1997).

The basic idea of smoothing lies in a local averaging procedure, which is constructed in such a way that it

is defined only from observations in a small neighborhood around z, since EFF -observations from points far

away from z will have, in general, very different mean values.10

10We have skipped most details regarding nonparametric regression. See, for instance Hardle (1990), for a good exposition.

13

More formally, the procedure can be defined as:

m(z) = S−1S∑

s=1

WS,s(z)EFFs (12)

where {WS,s(z)}Ss=1 denotes a sequence of weights which may depend on the whole vector {zs}S

s=1.

An alternative way of looking at the local averaging formula (12) is to suppose that the weights {WS,s} are

positive and sum to one for all z, i.e., S−1∑S

s=1 WS,s(z) = 1. Then m(z) is a least squares estimate at point z

since we can write m(z) as a solution to the following minimisation problem:

minθ

S−1S∑

s=1

WS,s(z)(EFFs − θ)2 = S−1S∑

s=1

WS,s(z)(EFFs − m(z))2. (13)

According to formula (13), we realise that the basic idea of local averaging is equivalent to the procedure of

finding a local weighted least squares estimate.

Nadaraya (1964) and Watson (1964) proposed the estimator of m(z) as a local average of EFFs, and can

be written as:

m(z) =∑S

s=1 EFFsKh(z − zs)∑Ss=1 Kh(z − zs)

(14)

which may be decomposed as

m(z) =S∑

s=1

EFFsWs(z) (15)

and

Ws(z) =Kh(z − zs)∑S

s=1 Kh(z − zs)(16)

where Kh(·) is a kernel function satisfying different properties.

The choice of kernel, Kh(·), may consist of several alternatives. For reasons of simplicity, we used a Gaussian

kernel, whose formula is based on the Gaussian density function:

Kh(z − zs) =1

(2π)1/2exp

[−1

2

(z − zs

h

)2]

(17)

where the quantity h is the bandwidth or smoothing parameter and controls the smoothness of m—likewise

the window width controls the smoothness of a moving average. Indeed, our choice of kernel is related to the

right amount of smoothing, i.e., the choice of bandwidth. This is the most crucial decision in nonparametric

regression. Every smoothing method has to be tuned by some smoothing parameter which balances the degree

of fidelity to data against the smoothness of the estimated curve. Although more popular techniques are

available, such as cross-validation, our focus will be on the more up-to-date approaches. Specifically, we follow

the contribution by Ruppert et al. (1995), who suggest plug-in rules. As stated by DiNardo et al. (1996), plug-in

methods do not exhibit the discretisation problems associated with cross-validation. Obviously, if we want a

smooth to be merely a descriptive device, the “by eye” technique may be satisfactory. However, this approach is

unsatisfactory in many circumstances. Thus, the practical implementation of any scatterplot, or nonparametric

14

regression smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the

smoothing parameter.

Graphs 2.a–2.f are nonparametric regressions of the efficiency scores on each of the explanatory variables

estimated by kernel smoothing, using the Nadaraya-Watson estimator. They generally support the hypothe-

sised signs of the regressions, although to varying extents. Regarding fiscal policy variables, we observe that

efficiency decreases with tax revenues, (TAXES), self-generated revenues (SELFG), and deficit (DEFICIT ),

as expected. However, grants (GRANTS) do not offer a clear pattern either towards increase or decrease. Yet

this occurs only for technical efficiency, whilst both cost and allocative efficiency do show a clear negative slope.

A plausible explanation, which we defer to the following paragraphs, could come from the existence of extreme

observations. In the case of loans and issued securities (SECLOAN), where the sign was hypothesised to be

positive, the pattern is less clear, although the visual snapshot partly suggests a negative relationship.

If we examine the particular details, we observe that the explanatory power of the grants variable (GRANTS)

exhibits a negative relationship for both allocative and, especially, cost efficiency. In addition, the relationship

does not exhibit remarkable ups and downs, rather it is linear. Our finding coincides with those of Silkman and

Young (1982), or De Borger and Kerstens (1996), who suggest that grants may not only encourage local service

provision, but also stimulate inefficiency, as the cost of inefficient behaviour is increasingly shared by national, or

regional, taxpayers. In the case of self-generated revenues (SELFG), the association is also negative, although

it exhibits some non-linearities: efficiency decreases steadily in the middle range, but the situation is less clear

at boundaries. This variable is highly related to tax revenues (TAXES). In fact, they only differ because

TAXES only accounts for revenues entirely generated via taxes.

In contrast, our variable with the strongest political content, i.e., the governing party share of votes

(V OTES) does exhibit a fuzzy pattern (Figure 2.f), and no conclusion may be drawn—in principle. Accordin-

gly, we cannot state that there is sufficient empirical evidence to corroborate the hypothesis that municipalities

managed by governments with a higher percentage of votes, more unlikely to face monitoring by other parties,

have fewer incentives to manage their resources efficiently.

4.2. Nonparametric bivariate density estimation

Unfortunately, the information provided by nonparametric regression is slightly skeletal. To fill out this in-

formation, we provide nonparametric estimation of the joint density functions of efficiency and each of the

explanatory variables. Its basic ideas closely resemble those underlying scatterplot smoothing (or nonpara-

metric regression), and therefore details have been deferred to appendix A. The main difference is that now

observations are counted and weighted, not in an interval band around each point, but in a two dimensional

elliptical band. For clearer interpretation, we also provide contour maps, where points linked by a contour have

the same density, and the contours are equally spaced.

This complementary approach is extremely informative, as it provides clear awareness of what exactly

underlies each regression line. Hence, we know exactly the probability mass or, put it another way, the empirical

evidence supporting each claimed sign for the differing associations.

The precise interpretation would suggest that when a negatively sloped regression line is observed, supporting

15

an inverse association between certain variable and efficiency, its corresponding bivariate density function should

exhibit probability mass also concentrated along a “hypothetical” negative slope in each contour map. In other

words, we would observe a collection of (possibly) consecutive bumps, possibly with high peaks, with probability

vanishing at other locations of the figure. In the likely event that these bumps were firmly concentrated along the

negative slope, it would indicate empirical evidence to support our prediction. This outcome would constitute

a parallelism with the case of (parametric) linear regression when a high value for the t-statistic is achieved.

On the other hand, if probability mass in the bivariate figure does not follow the path determined by the

nonparametric regression line, the scenario would mirror the case of linear regression when a poorer value for

the t-statistic is obtained.

Joint density functions are shown in Figures 3, 4 and 5 for all overall cost, technical and allocative efficiency,

respectively. Their respective contour maps are displayed in Figures 7, 6, and 8. Regarding technical efficiency,

a paradigm is constituted by Figure 4.b. Its nonparametric regression counterpart, i.e., Figure 2.b, shows an

unstable pattern, as the relationship between efficiency and transfers is negative except for those municipalities

with higher transfers, or grants, for which the relationship is positive. But Figure 4.b, together with its contour

plot in Figure 7.b, reveals that the units driving the regression line to shift upwards are very few, as probability

mass in the 3-d plot is scarce at its top-right end.

A similar pattern is revealed for securities and loans issued by municipalities, whose nonparametric regression

exhibits no clear pattern (see Figure 2.d). Yet its 3-d plots counterparts (Figures 4.d and 7.d) unmask what

determines this: for most municipalities we cannot infer any link, as they simply do not issue securities. For

others, a negative association is observed. But the probability mass supporting the latter assertion is quite

scarce, as revealed by a low number of contours (see Figure 7.d).

The remaining fiscal policy variables—TAXES (Figures 4.a and 7.a), SELFG (Figures 4.c and 7.c), and

DEFICIT (Figures 4.e and 7.e)—widely confirm what was revealed by regression, as probability mass has

a tendency to concentrate along the hypothetical negative slope diagonal. However, in all cases we notice a

remarkable amount of multi-modality. Related to this, we face the issue of bandwidth choice, which is critical

in nonparametric kernel density estimation, and has not yet been fully addressed in the bivariate case.11

Furthermore, we notice the difficulty in fitting a regression line of Y (or EFF , i.e., efficiency) on X (or z,

i.e., explanatory variables), given that all cases show substantial probability mass concentrations at boundaries.

Yet when analyzing cost (Figures 3 and 6) and allocative efficiencies (Figures 5 and 8) the observed patterns

are not exactly coincidental. In these cases the number of efficient municipalities is ostensibly lower, preventing

probability mass concentrations at the top—either left or right—of each sub-figure. This feature makes the

association between variables clearer in some instances. This is the case of grants and cost efficiency (Figures

3.b and 6.b), for which the negative relationship is apparent. In the case of allocative efficiency (Figures 5.b and

8.b) the negative relationship is also ostensible, yet probability mass does not concentrate so markedly along

the “hypothetical” negative slope.

In the other cases where a negative relationship was found between technical efficiency and the explanatory

11The best performers—in terms of balance between bias and variance—are those relying on plug-in methods, such as the onesput forward by Wand and Jones (1994).

16

variables, the outcome for the other types of efficiency is different, due to those technical efficient firms which

are cost and/or allocative inefficient. Hence, although both taxes and self-generated revenues exhibit a negative

association for some municipalities, this does not hold for all of them, for both cost (Figures 3.a, 3.c, 6.a and

6.c) and allocative (Figures 5.a, 3.c, 6.a and 6.c) efficiency.

Of special note is the case of V OTES, whose fuzzy nonparametric regression line (Figure 2.f) does not allow

us to infer any clear association between the votes of the governing party divided by population and efficiency.

Yet the nonparametric bivariate density estimation reveals that the number of observations with V OTES > 1

is very low. If we disregard these municipalities, and consider only those with V OTES < 1, which are those

with the overwhelming majority, the apparent relationship is negative for all types of inefficiency. Thus, it

seems that our “preferred” hypothesis is accepted, as governing parties with percentage of votes might be facing

strong monitoring from other parties and coalitions, which contributes to enhancing efficiency.

5. Concluding remarks

This article has analyzed the efficiency of Valencian (Spain) local governments, with an explicit attempt at mea-

suring not only economic (cost) efficiency but also its decomposition into its allocative and technical components.

Such a decomposition turns out to be of paramount importance, since most inefficiencies are attributable to

a non-optimal choice of input mix. Put another way, a reallocation of inputs could lead to a substantial cost

reduction, given their relative prices.

Our linear programming techniques also allow specific input and output inefficiencies to be detected, i.e.,

input excesses and output underprovisions (or shortfalls). Except for current transfers, all input variables show

similar excesses. Disparities are more marked on the output side, for which both number of lighting points and

street infrastructure surface area, essentially related to capital expenditure, face the greatest underprovisions.

Indeed, street infrastructure surface area is more important than what one might a priori expect, provided it

also proxies for accesses to population centers, street cleaning, or supply of drinking water to households. It is

also important to bear in mind that our output indicators include a quality variable, of paramount significance

in our setting.

Results do also vary according to local governments’ size, as large municipalities generally perform better.

Yet this result is not entirely attributable to a more proficient management. Although our findings indicate

that there is a wide margin available to public managers for optimization in the use of public resources, some of

these inefficiencies might be caused by variables disregarded when measuring efficiency; some partly lie within

local governments’ control, yet others remain outside it. Specifically, we considered a set of both fiscal policy

and political variables out of which self-generated revenues, grants, deficit, and votes of the governing party

over total population were found to have a negative impact on efficiency, although they varied with the type

of efficiency considered. More precisely, the empirical evidence was quite relevant in the case of overall cost

efficiency for unconditional grants received from higher layers of government, and votes of the governing party

over total population.

The latter results were obtained via nonparametric smoothing techniques, instead of either OLS or Tobit

17

models. This is important due to the special distributional features of DEA efficiency scores which, by cons-

truction, are bounded by zero and unity. As we use linear programming techniques, a mass of efficiency scores

achieves the upper bound. Although some authors have attempted to address this issue, they did not consider

the statistical dependency of efficiency scores, which leads to the violation of important hypotheses. Alterna-

tively, as our techniques are fully nonparametric, we neither face the skewness nor the statistical dependency

problem.

A. Nonparametric estimation of bivariate density functions

To estimate joint density functions, in which the OX axis represents the explanatory variable and the OY

axis represents the dependent variable, i.e., efficiency, we also chose nonparametric techniques. Again, one of

the most popular alternatives is kernel smoothing. The basics are quite similar to scatterplot smoothing—or

nonparametric regression.

While the approach to smooth data is exactly the same (kernel smoothing), the other two decisions are not

exactly coincidental. Regarding the choice of kernel, we consider here, following Wand and Jones (1995) and, in

his applied work, Deaton (1989), the Epanechnikov kernel. We proceed with this for efficiency considerations.

Its expression is as follows:

f(x;H) = S−1S∑

s=1

KH(x − vs) (18)

where vs = (zs, EFFs), x = (x1, x2) is the point of evaluation, H is a d×d (in our case, 2×2) bandwidth matrix,

and KH is a kernel function:

KH(x) = |H|−1/2K(H−1/2x) (19)

We consider H ∈ D, where D ⊆ F defines the subclass of diagonal positive definite matrices 2×2 (D =

{diag(h21, h

22) : h1, h2 > 0}). Hence, for H ∈ D, we have H = diag(h2

1, h22).

According to the above statements, provided h = (h1, h2), the bivariate density function to be estimated is:

f(x;h) = (nh1h2)−1S∑

s=1

K(x1 − zs

h1,x2 − EFFs

h2) (20)

Finally, we have chosen the Epanechnikov kernel, whose expression for the bivariate case is as follows:

Ke(x) =

12c−1

d (d + 2)(1 − xT x) if xT x < 1

0 otherwise.(21)

where cd is the volume of the d-dimensional unit sphere: c1 = 2, c2 = π, c3 = 4π/3, etc.

Unfortunately, we have to deal with a problem that has still not been satisfactorily addressed in the

literature—namely, the choice of bandwidth. In this case, the state of the art is in a much more prelimi-

nary state than either in the univariate case or that of nonparametric regression. One of the most up-to-date

contributions is the work by Wand and Jones (1994), also based on plug-in methods, which is precisely our

18

choice. Although previous research considers by-eye criteria (Deaton, 1989), we do not completely agree with

this view, as it partly undermines the impartiality of the analysis. When possible, data-driven methods are

preferable.

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analyses: A comparative study of NSW local government. Applied Economics, 34(4):453–464.

21

Table 1: Descriptive statistics for the relevant variables (1995)Inputsa Mean Std.dev.Wages and salaries (X1) 117335.95 198594.00Expenditure on goods and services (X2) 94683.56 153212.62Current transfers (X3) 17492.75 35637.52Capital transfers (X4) 1587.99 7005.55Capital expenditure (X5) 74603.31 115218.63Outputs Mean Std.dev.Population (Y1) 4730.18 7607.53Number of lighting points (Y2) 594.52 1038.66Tons of waste (Y3) 13093.19 75751.95Street infrastructure surface areab(Y4) 126010.25 196552.32Registered surface area of public parksb(Y5) 15957.28 32503.52Quality (Y6) 2.632 0.308

a In thousands of 1995 pesetas.b In square metres.

Table 2: Output indicators based on the minimum services providedMinimum services provided Output indicators

Public street lighting Number of lighting pointsCemetery Total population

Waste collection Waste collectedStreet cleaning Street infrastructure surface area

Supply of drinking water to households Population, street infrastructure surface areaAccess to population centers Street infrastructure surface area

Surfacing of public roads Street infrastructure surface areaRegulation of food and drink Total population

22

Tab

le3:

Sum

mar

yst

atis

tics

for

effici

ency

mea

sure

sby

popu

lati

onsi

zes

(N=

414)

Sta

ndard

%ofeffi

cien

tIn

effici

ency

Siz

ecl

ass

Mea

ndev

iati

on

Skew

nes

sK

urt

osi

sM

inim

um

Maxim

um

obse

rvati

ons

All

size

s0.5

31

0.2

46

0.3

73

−0.7

46

0.0

14

1.0

00

32/414(7

.73%

)P

OP

<1,0

00

0.4

28

0.2

32

1.0

16

0.4

56

0.0

14

1.0

00

9/161(5

.59%

)O

ver

all

cost

1,0

00≤

PO

P<

5,0

00

0.4

95

0.2

02

0.4

09

−0.0

91

0.0

80

1.0

00

4/144(2

.78%

)5,0

00≤

PO

P<

20,0

00

0.6

88

0.1

91

0.0

42

−0.7

90

0.2

60

1.0

00

8/82(9

.76%

)P

OP

≥20,0

00

0.8

61

0.1

59

−0.9

42

−0.0

84

0.4

70

1.0

00

11/27(4

0.7

4%

)A

llsi

zes

0.8

01

0.2

10

−0.8

00

−0.3

77

0.1

49

1.0

00

144/414(3

4.7

8%

)P

OP

<1,0

00

0.7

92

0.2

25

−0.6

41

−0.9

57

0.2

32

1.0

00

66/161(4

0.9

9%

)Tec

hnic

al

1,0

00≤

PO

P<

5,0

00

0.7

49

0.2

09

−0.6

07

−0.2

40

0.1

49

1.0

00

30/144(2

0.8

3%

)5,0

00≤

PO

P<

20,0

00

0.8

55

0.1

70

−1.1

53

0.5

61

0.3

71

1.0

00

30/82(3

6.5

9%

)P

OP

≥20,0

00

0.9

68

0.0

64

−2.0

03

3.0

79

0.7

73

1.0

00

18/27(6

6.6

7%

)A

llsi

zes

0.6

58

0.2

19

−0.2

86

−0.6

97

0.0

14

1.0

00

32/414(7

.73%

)P

OP

<1,0

00

0.5

44

0.2

25

0.2

80

−0.5

43

0.0

14

1.0

00

9/161(5

.59%

)A

lloca

tive

1,0

00≤

PO

P<

5,0

00

0.6

58

0.1

75

−0.2

42

−0.5

56

0.2

43

1.0

00

4/144(2

.78%

)5,0

00≤

PO

P<

20,0

00

0.8

05

0.1

41

−0.5

74

−0.3

07

0.4

41

1.0

00

8/82(9

.76%

)P

OP

≥20,0

00

0.8

87

0.1

38

−1.1

82

0.4

27

0.5

37

1.0

00

11/27(4

0.7

4%

)

23

Tab

le4:

Sum

mar

yst

atis

tics

for

spec

ific

inpu

tin

effici

ency

a

Sta

ndard

Vari

able

Siz

ecl

ass

Mea

ndev

iati

on

Med

ian

Kurt

osi

sSkew

nes

sM

inim

um

Maxim

um

All

size

s0.2

12

0.2

19

0.1

64

−0.4

18

0.7

62

0.0

00

0.8

81

PO

P<

1,0

00

0.2

27

0.2

36

0.1

67

−0.8

97

0.5

96

0.0

00

0.8

81

X1

1,0

00≤

PO

P<

5,0

00

0.2

57

0.2

14

0.2

11

−0.2

08

0.6

29

0.0

00

0.8

51

5,0

00≤

PO

P<

20,0

00

0.1

55

0.1

83

0.1

14

0.0

68

1.0

67

0.0

00

0.6

29

PO

P≥

20,0

00

0.0

62

0.1

25

0.0

00

7.1

78

2.5

86

0.0

00

0.5

27

All

size

s0.2

21

0.2

26

0.1

70

−0.4

97

0.7

20

0.0

00

0.9

22

PO

P<

1,0

00

0.2

37

0.2

45

0.2

20

−1.0

09

0.5

28

0.0

00

0.9

22

X2

1,0

00≤

PO

P<

5,0

00

0.2

74

0.2

24

0.2

46

−0.4

38

0.5

29

0.0

00

0.9

00

5,0

00≤

PO

P<

20,0

00

0.1

55

0.1

77

0.1

21

0.6

49

1.1

23

0.0

00

0.6

98

PO

P≥

20,0

00

0.0

49

0.1

02

0.0

00

6.0

90

2.4

54

0.0

00

0.4

15

All

size

s0.2

47

0.2

61

0.1

76

−0.4

50

0.8

04

0.0

00

0.9

72

PO

P<

1,0

00

0.2

66

0.2

85

0.1

81

−0.7

73

0.6

89

0.0

00

0.9

72

X3

1,0

00≤

PO

P<

5,0

00

0.3

08

0.2

57

0.3

12

−0.6

70

0.5

13

0.0

00

0.9

08

5,0

00≤

PO

P<

20,0

00

0.1

71

0.2

07

0.1

14

0.3

85

1.1

81

0.0

00

0.7

32

PO

P≥

20,0

00

0.0

44

0.0

93

0.0

00

8.9

20

2.7

97

0.0

00

0.4

12

All

size

s0.1

17

0.2

67

0.0

00

3.5

61

2.2

17

0.0

00

1.0

00

PO

P<

1,0

00

0.1

42

0.3

02

0.0

00

1.8

50

1.8

66

0.0

00

1.0

00

X4

1,0

00≤

PO

P<

5,0

00

0.1

20

0.2

62

0.0

00

3.2

54

2.1

10

0.0

00

1.0

00

5,0

00≤

PO

P<

20,0

00

0.0

85

0.2

17

0.0

00

9.7

98

3.1

39

0.0

00

1.0

00

PO

P≥

20,0

00

0.0

49

0.1

96

0.0

00

20.9

02

4.4

86

0.0

00

0.9

75

All

size

s0.2

46

0.2

48

0.1

84

−0.8

86

0.6

01

0.0

00

0.8

51

PO

P<

1,0

00

0.2

64

0.2

67

0.2

29

−1.3

11

0.4

24

0.0

00

0.8

42

X5

1,0

00≤

PO

P<

5,0

00

0.2

87

0.2

39

0.2

46

−0.6

80

0.5

14

0.0

00

0.8

51

5,0

00≤

PO

P<

20,0

00

0.1

95

0.2

25

0.1

16

−0.3

54

0.8

90

0.0

00

0.7

81

PO

P≥

20,0

00

0.0

81

0.1

49

0.0

00

2.5

55

1.8

25

0.0

00

0.5

35

aSpec

ific

inputin

effici

ency

incl

udes

both

the

radia

lre

duct

ion

ofin

puts

plu

sth

ein

putsl

ack

,and

refe

rsto

the

magnit

ude

ofin

puts

“to

gain

”.

24

Tab

le5:

Sum

mar

yst

atis

tics

for

spec

ific

outp

utin

effici

ency

a

Sta

ndard

Vari

able

Siz

ecl

ass

Mea

ndev

iati

on

Med

ian

Kurt

osi

sSkew

nes

sM

inim

um

Maxim

um

All

size

s0.9

33

0.1

57

1.0

00

11.9

84

−3.2

14

0.0

10

1.0

00

PO

P<

1,0

00

0.9

68

0.1

11

1.0

00

30.9

31

−5.1

00

0.0

89

1.0

00

Y1

1,0

00≤

PO

P<

5,0

00

0.9

12

0.1

79

1.0

00

9.1

27

−2.7

99

0.0

10

1.0

00

5,0

00≤

PO

P<

20,0

00

0.8

99

0.1

90

1.0

00

6.3

07

−2.4

03

0.0

40

1.0

00

PO

P≥

20,0

00

0.9

41

0.1

19

1.0

00

4.3

59

−2.1

82

0.5

45

1.0

00

All

size

s0.8

18

0.2

80

1.0

00

1.2

09

−1.4

88

0.0

00

1.0

00

PO

P<

1,0

00

0.8

44

0.2

81

1.0

00

2.3

44

−1.8

56

0.0

00

1.0

00

Y2

1,0

00≤

PO

P<

5,0

00

0.7

35

0.2

92

0.8

09

−0.4

85

−0.7

58

0.0

00

1.0

00

5,0

00≤

PO

P<

20,0

00

0.8

67

0.2

56

1.0

00

4.5

19

−2.2

18

0.0

00

1.0

00

PO

P≥

20,0

00

0.9

65

0.1

07

1.0

00

19.5

47

−4.2

40

0.4

65

1.0

00

All

size

s0.9

14

0.1

73

1.0

00

6.6

72

−2.4

31

0.0

07

1.0

00

PO

P<

1,0

00

0.9

47

0.1

34

1.0

00

12.1

56

−3.1

62

0.0

86

1.0

00

Y3

1,0

00≤

PO

P<

5,0

00

0.8

91

0.1

95

1.0

00

5.5

10

−2.2

48

0.0

07

1.0

00

5,0

00≤

PO

P<

20,0

00

0.8

82

0.1

99

1.0

00

3.7

40

−1.8

52

0.0

09

1.0

00

PO

P≥

20,0

00

0.9

34

0.1

43

1.0

00

2.2

50

−1.9

22

0.5

22

1.0

00

All

size

s0.7

19

0.3

88

1.0

00

−0.9

20

−0.8

96

0.0

00

1.0

00

PO

P<

1,0

00

0.6

79

0.4

30

1.0

00

−1.2

90

−0.7

60

0.0

00

1.0

00

Y4

1,0

00≤

PO

P<

5,0

00

0.7

21

0.3

66

1.0

00

−1.0

34

−0.8

06

0.0

00

1.0

00

5,0

00≤

PO

P<

20,0

00

0.7

36

0.3

57

1.0

00

−0.6

19

−0.9

55

0.0

00

1.0

00

PO

P≥

20,0

00

0.8

87

0.2

83

1.0

00

4.7

00

−2.4

51

0.0

25

1.0

00

All

size

s0.9

69

0.1

00

1.0

00

60.0

96

−6.9

36

0.0

01

1.0

00

PO

P<

1,0

00

0.9

73

0.0

71

1.0

00

10.9

24

−3.1

88

0.5

66

1.0

00

Y5

1,0

00≤

PO

P<

5,0

00

0.9

61

0.1

24

1.0

00

45.4

46

−6.3

40

0.0

01

1.0

00

5,0

00≤

PO

P<

20,0

00

0.9

69

0.1

14

1.0

00

64.8

70

−7.6

81

0.0

06

1.0

00

PO

P≥

20,0

00

0.9

92

0.0

36

1.0

00

24.1

30

−4.8

45

0.8

18

1.0

00

All

size

s0.9

84

0.1

07

1.0

00

63.4

20

−7.8

04

0.0

13

1.0

00

PO

P<

1,0

00

0.9

82

0.1

02

1.0

00

57.5

03

−7.2

41

0.0

39

1.0

00

Y6

1,0

00≤

PO

P<

5,0

00

0.9

80

0.1

23

1.0

00

52.7

57

−7.1

57

0.0

13

1.0

00

5,0

00≤

PO

P<

20,0

00

0.9

89

0.1

02

1.0

00

81.9

99

−9.0

55

0.0

75

1.0

00

PO

P≥

20,0

00

1.0

00

0.0

01

1.0

00

27.0

00

−5.1

96

0.9

93

1.0

00

aSpec

ific

outp

ut

ineffi

cien

cy,

incl

udes

both

the

radia

lex

pansi

on

of

outp

uts

plu

sth

eoutp

ut

slack

,and

refe

rsto

the

magnit

ude

ofoutp

uts

“ach

ieved

”.

Conse

quen

tly,

figure

scl

ose

rto

1su

gges

tabse

nce

ofoutp

ut

short

fall.

25

Fig

ure

1:Tuk

ey’s

box

plot

sof

effici

ency

scor

es(o

vera

llco

st,te

chni

cal,

and

allo

cati

ve)

bysi

zecl

asse

s

AL

LS

1S

2S

3S

40

.0

0.2

0.4

0.6

0.8

1.0

a)O

vera

llco

st

AL

LS

1S

2S

3S

40

.00

0.2

5

0.5

0

0.7

5

1.0

0

b)

Tec

hnic

al

AL

LS

1S

2S

3S

40

.0

0.2

0.4

0.6

0.8

1.0

c)A

lloca

tive

All

size

s:al

lm

unic

ipal

itie

s.S1

:m

unic

ipal

itie

sw

ith

PO

P<

1,00

0.S2

:m

unic

ipal

itie

sw

ith

1,00

0≤

PO

P<

5,00

0.S3

:m

unic

ipal

itie

sw

ith

5,00

0≤

PO

P<

20,0

00.

S4:

mun

icip

alit

ies

wit

hP

OP

≥20

,000

.

26

Fig

ure

2:E

ffici

ency

dete

rmin

ants

,N

adar

aya-

Wat

son

nonp

aram

etri

cre

gres

sion

(ove

rall

cost

,te

chni

cal,

and

allo

cati

veeffi

cien

cy)

0

0.2

0.4

0.6

0.81

12

34

5

Efficiency

a)T

AX

ES

0

0.2

0.4

0.6

0.81

34

56

7

Efficiency

b)G

RA

NT

S

0

0.2

0.4

0.6

0.81

11.5

22.5

33.5

44.5

55.5

Efficiency

c)S

EL

FG

0

0.2

0.4

0.6

0.81

01

23

45

67

8

Efficiency

d)S

EC

LO

AN

0

0.2

0.4

0.6

0.81

0.6

0.8

11.2

1.4

1.6

1.8

Efficiency

e)D

EF

IC

IT

0

0.2

0.4

0.6

0.81

00.5

11.5

2

Efficiency

f)V

OT

ES

Over

all

cost

----

--Tec

hnic

al—

—A

lloca

tive······

Nonpara

met

ric

ker

nel

regre

ssio

n,G

auss

ian

ker

nel

,bandw

idth

sch

ose

nacc

ord

ing

toth

eplu

g-in

rule

sin

Rupper

tet

al.

(1995)

(hT

AX

ES

=0.1

926,h

GR

AN

TS

=0.3

762,

hS

EL

FG

=0.0

808,h

SE

CL

OA

N=

0.4

089,h

DE

FIC

IT

=0.0

886).

27

Fig

ure

3:E

ffici

ency

dete

rmin

ants

,jo

int

dens

itie

s,ov

eral

lco

steffi

cien

cy

1

2

3

4

5

TAXES

0.2

0.4

0.6

0.8

1

Efficiency

0

0.51

1.52

2.5

a)T

AX

ES

3

4

5

6

7

GRANTS

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

0

0.51

1.52

2.5

b)G

RA

NT

S

11.522.533.544.555.5

SELFG

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

0

0.51

1.52

2.5

c)S

EL

FG

12

34

56

78

SECLOAN

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

00.51

1.52

2.53

3.54

d)S

EC

LO

AN

0.8

1

1.2

1.4

1.6

1.8

DEFICIT

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

0246810

12

14

e)D

EF

IC

IT

0.5

1

1.5

2

VOTES

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

01234567

f)V

OT

ES

Den

siti

eses

tim

ate

dnonpara

met

rica

lly

by

mea

ns

ofE

panec

hnik

ov

ker

nel

,bandw

idth

sch

ose

nacc

ord

ing

toW

and

and

Jones

(1994).

Diff

eren

tbandw

idth

sare

esti

mate

dfo

rea

chco

-ord

inate

dir

ecti

on.

h(T

AX

ES) T

AX

ES

=0.1

727,h(T

AX

ES) E

fficie

ncy

=0.0

513,h(G

RA

NT

S) G

RA

NT

S=

0.1

482,h(G

RA

NT

S) E

fficie

ncy

=0.0

653,h(S

EL

FG

) SE

LF

G=

0.1

329,

h(S

EL

FG

) Effi

cie

ncy

=0.0

849,h(S

EC

LO

AN

) SE

CL

OA

N=

0.2

768,h(S

EC

LO

AN

) Effi

cie

ncy

=0.0

884,h(D

EF

IC

IT

) DE

FIC

IT

=0.0

325,h(D

EF

IC

IT

) Effi

cie

ncy

=0.0

808,

h(V

OT

ES) V

OT

ES

=0.0

641,h(V

OT

ES) E

fficie

ncy

=0.0

815.

28

Fig

ure

4:E

ffici

ency

dete

rmin

ants

,jo

int

dens

itie

s,te

chni

caleffi

cien

cy

1

2

3

4

5

TAXES

0.2

0.4

0.6

0.8

1

Efficiency

01234567

a)T

AX

ES

3

4

5

6

7

GRANTS

0.2

0.4

0.6

0.8

1

Efficiency

0123456

b)G

RA

NT

S

11.522.533.544.555.5

SELFG

0.2

0.4

0.6

0.8

1

Efficiency

01234567

c)S

EL

FG

12

34

56

78

SECLOAN

0.2

0.4

0.6

0.8

1

Efficiency

01234567

d)S

EC

LO

AN

0.8

1

1.2

1.4

1.6

1.8

DEFICIT

0.2

0.4

0.6

0.8

1

Efficiency

05

10

15

20

25

e)D

EF

IC

IT

0.5

1

1.5

2

VOTES

0.2

0.4

0.6

0.8

1

Efficiency

0246810

12

14

f)V

OT

ES

Den

siti

eses

tim

ate

dnonpara

met

rica

lly

by

mea

ns

ofE

panec

hnik

ov

ker

nel

,bandw

idth

sch

ose

nacc

ord

ing

toW

and

and

Jones

(1994).

Diff

eren

tbandw

idth

sare

esti

mate

dfo

rea

chco

-ord

inate

dir

ecti

on.

h(T

AX

ES) T

AX

ES

=0.1

473,h(T

AX

ES) E

fficie

ncy

=0.0

631,h(G

RA

NT

S) G

RA

NT

S=

0.1

718,h(G

RA

NT

S) E

fficie

ncy

=0.0

606,h(S

EL

FG

) SE

LF

G=

0.1

380,

h(S

EL

FG

) Effi

cie

ncy

=0.0

618,h(S

EC

LO

AN

) SE

CL

OA

N=

0.3

115,h(S

EC

LO

AN

) Effi

cie

ncy

=0.0

801,h(D

EF

IC

IT

) DE

FIC

IT

=0.0

350,h(D

EF

IC

IT

) Effi

cie

ncy

=0.0

690,

h(V

OT

ES) V

OT

ES

=0.0

747,h(V

OT

ES) E

fficie

ncy

=0.0

656.

29

Fig

ure

5:E

ffici

ency

dete

rmin

ants

,jo

int

dens

itie

s,al

loca

tive

effici

ency

1

2

3

4

5

TAXES

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

0

0.51

1.52

2.5

a)T

AX

ES

3

4

5

6

7

GRANTS

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

00.51

1.52

2.53

b)G

RA

NT

S

11.522.533.544.555.5

SELFG

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

00.51

1.52

2.53

c)S

EL

FG

12

34

56

78

SECLOAN

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

00.51

1.52

2.53

d)S

EC

LO

AN

0.8

1

1.2

1.4

1.6

1.8

DEFICIT

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

0246810

12

e)D

EF

IC

IT

0.5

1

1.5

2

VOTES

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

01234567

f)V

OT

ES

Den

siti

eses

tim

ate

dnonpara

met

rica

lly

by

mea

ns

ofE

panec

hnik

ov

ker

nel

,bandw

idth

sch

ose

nacc

ord

ing

toW

and

and

Jones

(1994).

Diff

eren

tbandw

idth

sare

esti

mate

dfo

rea

chco

-ord

inate

dir

ecti

on.

h(T

AX

ES) T

AX

ES

=0.1

339,h(T

AX

ES) E

fficie

ncy

=0.0

686,h(G

RA

NT

S) G

RA

NT

S=

0.1

449,h(G

RA

NT

S) E

fficie

ncy

=0.0

562,h(S

EL

FG

) SE

LF

G=

0.1

341,

h(S

EL

FG

) Effi

cie

ncy

=0.0

676,h(S

EC

LO

AN

) SE

CL

OA

N=

0.2

877,h(S

EC

LO

AN

) Effi

cie

ncy

=0.0

819,h(D

EF

IC

IT

) DE

FIC

IT

=0.0

339,

h(D

EF

IC

IT

) Effi

cie

ncy

=0.0

675,h

(VO

TE

S) V

OT

ES

=0.0

656,h(V

OT

ES) E

fficie

ncy

=0.0

662.

30

Fig

ure

6:E

ffici

ency

dete

rmin

ants

,jo

int

dens

itie

s,ov

eral

lco

steffi

cien

cy(c

onto

urpl

ots)

12

34

5

TAXES

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

a)T

AX

ES

34

56

7

GRANTS

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

b)G

RA

NT

S

11.5

22.5

33.5

44.5

55.5

SELFG

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

c)S

EL

FG

01

23

45

67

8

SECLOAN

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

d)S

EC

LO

AN

0.6

0.8

11.2

1.4

1.6

1.8

DEFICIT

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

e)D

EF

IC

IT

00.5

11.5

2

VOTES

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

f)V

OT

ES

31

Fig

ure

7:E

ffici

ency

dete

rmin

ants

,jo

int

dens

itie

s,te

chni

caleffi

cien

cy(c

onto

urpl

ots)

12

34

5

TAXES

00.2

0.4

0.6

0.8

1

Efficiency

a)T

AX

ES

34

56

7

GRANTS

00.2

0.4

0.6

0.8

1

Efficiency

b)G

RA

NT

S

11.5

22.5

33.5

44.5

55.5

SELFG

00.2

0.4

0.6

0.8

1

Efficiency

c)S

EL

FG

01

23

45

67

8

SECLOAN

00.2

0.4

0.6

0.8

1

Efficiency

d)S

EC

LO

AN

0.6

0.8

11.2

1.4

1.6

1.8

DEFICIT

00.2

0.4

0.6

0.8

1

Efficiency

e)D

EF

IC

IT

00.5

11.5

2

VOTES

00.2

0.4

0.6

0.8

1

Efficiency

f)V

OT

ES

32

Fig

ure

8:E

ffici

ency

dete

rmin

ants

,jo

int

dens

itie

s,al

loca

tive

effici

ency

(con

tour

plot

s)

12

34

5

TAXES

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

a)T

AX

ES

34

56

7

GRANTS

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

b)G

RA

NT

S

11.5

22.5

33.5

44.5

55.5

SELFG

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

c)S

EL

FG

01

23

45

67

8

SECLOAN

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

d)S

EC

LO

AN

0.6

0.8

11.2

1.4

1.6

1.8

DEFICIT

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

e)D

EF

IC

IT

00.5

11.5

2

VOTES

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency

f)V

OT

ES

33